Dynamic mode decomposition using a Kalman filter for parameter estimation
Source abstract
Abstract
A novel dynamic mode decomposition (DMD) method based on a Kalman filter is proposed. This paper explains the fast algorithm of the proposed Kalman filter DMD (KFDMD) in combination with truncated proper orthogonal decomposition for many-degree-of-freedom problems. Numerical experiments reveal that KFDMD can estimate eigenmodes more precisely compared with standard DMD or total least-squares DMD (tlsDMD) methods for the severe noise condition if the nature of the observation noise is known, though tlsDMD works better than KFDMD in the low and medium noise level. Moreover, KFDMD can track the eigenmodes precisely even when the system matrix varies with time similar to online DMD, and this extension is naturally conducted owing to the characteristics of the Kalman filter. In summary, the KFDMD is a promising tool with strong antinoise characteristics for analyzing sequential datasets.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Model Reduction and Neural Networks · Structural Health Monitoring Techniques · Probabilistic and Robust Engineering Design
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Aerospace Engineering, Graduate School of Engineering, Tohoku University 1 , Sendai, Miyagi 9808579, Japan
Presto, JST 2 , Sendai, Miyagi 9808579, Japan
Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency 3 , Sagamihara, Kanagawa 2525210, Japan
Funding
Precursory Research for Embryonic Science and Technology
References (29)
Show source-provided references
1. Modal analysis of fluid flows: An overview10.2514/1.j056060 ↗
2. Model reduction for compressible flows using POD and Galerkin projection10.1016/j.physd.2003.03.001 ↗
3. The proper orthogonal decomposition in the analysis of turbulent flows10.1146/annurev.fl.25.010193.002543 ↗
4. Global linear instability10.1146/annurev-fluid-122109-160705 ↗
5. Global stability analysis method to numerically predict precursor of breakdown voltage
6. Assessment of global linear stability analysis using a time-stepping approach for compressible flows10.1002/fld.4166 ↗
7. Dynamic mode decomposition of numerical and experimental data10.1017/s0022112010001217 ↗
8. Extraction and reconstruction of individual vortex-shedding mode from bistable flow
9. Low-frequency dynamics in a shock-induced separated flow10.1017/jfm.2016.557 ↗
10. Numerical investigation of transonic buffet on a three-dimensional wing using incremental mode decomposition
11. On dynamic mode decomposition: Theory and applications10.3934/jcd.2014.1.391 ↗
12. Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition10.1007/s00348-016-2127-7 ↗
13. Improving separation control with noise-robust variants of dynamic mode decomposition
14. De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets
15. Sparsity-promoting dynamic mode decomposition10.1063/1.4863670 ↗
16. Dynamic mode decomposition for large and streaming datasets10.1063/1.4901016 ↗
17. Preconditioned dynamic mode decomposition and mode selection algorithms for large datasets using incremental proper orthogonal decomposition10.1063/1.4996024 ↗
18. On-the-fly algorithm for dynamic mode decomposition using incremental singular value decomposition and total least squares
19. Online dynamic mode decomposition for time-varying systems
20. A new approach to linear filtering and prediction problems10.1115/1.3662552 ↗
21. Linear observer synthesis for nonlinear systems using Koopman operator framework10.1016/j.ifacol.2016.10.250 ↗
22. Koopman operator framework for constrained state estimation
23. Principal component analysis with noisy and/or missing data10.1086/668105 ↗
24. Activities of computational fluid dynamics in japan: Compressible flow simulations
25. Compact finite difference schemes with spectral-like resolution10.1016/0021-9991(92)90324-r ↗
26. Efficiency improvement of unified implicit relaxation/time integration algorithms10.2514/2.676 ↗
27. ADI-SGS scheme on ideal magnetohydrodynamics10.1016/j.jcp.2009.01.032 ↗
28. Mechanisms for laminar separated-flow control using dielectric-barrier-discharge plasma actuator at low Reynolds number10.1063/1.4935357 ↗
29. Extended-Kalman-filter-based dynamic mode decomposition for simultaneous system identification and denoising